Question

The function f(x) = 5x arctan(8x) is represented as power series f(x) = sigma(n=0 to inf) c_n x^n

Find the coefficients in power series:
c0 = 40
c1= -2560/3
c2=163840/5
c3=-10485760/7
c4=671088640/9

These are what i found and they're wrong. Any help?

Answer 1

Is this an online-submission-type of problem?

If that's the case, I think the reason your answer isn't being accepted is because \(c_2\) isn't completely reduced. The other four coefficients are right, though.

Checked with WolframAlpha: http://www.wolframalpha.com/input/?i=PowerSeries%5B5x*InverseTan%5B8x%5D%5D (click on "more terms")

Answer 2

Yes, it is. Is there anything to do to reduce it?

Answer 3

The numerator is divisible by 5.

Answer 4

i.e.
\[\frac{10}{5}=\frac{5\cdot2}{5}=2\]

Answer 5

Oh alright. I'll try that

Answer 6

Still does not work. So i guess there might just be an error

Answer 7

The next best explanation I can think of is that you're told the series is
\[f(x)=\sum_{n=0}^\infty c_nx^n=c_0+c_1x+c_2x^2+c_3x^3+c_4x^4+\cdots\]
According to my link (and your work),
\[c_0=0\\
c_1=0\\
c_2=40\\
c_3=0\\
c_4=-\frac{2560}{3}\]

Answer 8

You must have mixed up the subscript with the order the non-zero coefficients appear in, as opposed to the degree of the x term they're paired with.

Answer 9

Oh, there you go. Got it! I ignored cn x^n. Thanks a bunch!

Answer 10

You're welcome!